PlatosErbe
25-07-2008, 13:01
Hallo,
schreibe gerade einen Anhang für meine Diplomarbeit. Da leite ich zwei Formeln her. Die Herleitungen stehen in 2 align-Umgebungen. Jede align-Umgebung enthält ca. 6-7 Zeilen. Ich will das die 2 align-Umgebung direkt unter der ersten anfängt und dann umgebrochen wird. Im Moment entsteht aber zwischen beiden Umgebungen ein riesengroßer Abstand und die 2 Umgebung bricht schon nach der ersten um. Habt ihr mich verstanden?
Weiß jemand ne Lösung?
Außerdem würde mich noch interessieren wie ich eine Formel links am Text ausrichte?
Danke im Voraus Gruß der Erbe
Code:
\documentclass[a4paper,11pt,twoside,german]{scrreprt}
\usepackage{amssymb,amsmath}
\usepackage[ngerman]{babel}
\parindent=0cm
\setlength{\voffset}{-10mm}
\setlength{\topmargin}{5mm}
\oddsidemargin=0mm
\evensidemargin=0mm
\setlength{\textwidth}{159.2mm}
\textheight=245mm
\usepackage{setspace}
\onehalfspacing
\begin{document}
\bigskip
\textbf{\Large{Herleitung der Ableitung von $f(a_{zu,i})$}}
\begin{align*}
& f(a_{zu,i}) = \dfrac{3 \, c_{W} \, \rho_{L} \, A_{Proj2} \, l_{LW2}}{2 \, b_{W} \, t_{W}^{2}} \left[a_{zu,i} \, \left(t_{R} + \sqrt{\dfrac{(s - a_{zu,i} \, t_{R}^{2})}{a_{zu,i}}}\right)\right]^{2} - \sigma_{b,zul}\\
& f(a_{zu,i}) = \dfrac{3 \, c_{W} \, \rho_{L} \, A_{Proj2} \, l_{LW2}}{2 \, b_{W} \, t_{W}^{2}} \left[a_{zu,i}^{2} \, t_{R}^{2} + 2 \, a_{zu,i}^{2} \, t_{R} \, \sqrt{\dfrac{(s - a_{zu,i} \, t_{R}^{2})}{a_{zu,i}}} + a_{zu,i}^{2} \, \dfrac{(s - a_{zu,i} \, t_{R}^{2})}{a_{zu,i}}\right] - \sigma_{b,zul}\\
& f(a_{zu,i}) = \dfrac{3 \, c_{W} \, \rho_{L} \, A_{Proj2} \, l_{LW2}}{2 \, b_{W} \, t_{W}^{2}} \left[a_{zu,i}^{2} \, t_{R}^{2} + 2 \, a_{zu,i}^{2} \, t_{R} \, \sqrt{\dfrac{(s - a_{zu,i} \, t_{R}^{2})}{a_{zu,i}}} + a_{zu,i} \, s - a_{zu,i}^{2} \, t_{R}^{2} \right] - \sigma_{b,zul}
\intertext{mit:}
& \left(\sqrt{\dfrac{(s - a_{zu,i} \, t_{R}^{2})}{a_{zu,i}}}\right)' = \dfrac{1}{2} \, \left(\dfrac{(s - a_{zu,i} \, t_{R}^{2})}{a_{zu,i}}\right)^{-\dfrac{1}{2}} \cdot \left(\dfrac{-t_{R}^{2} \, a_{zu,i} - 1 \cdot (s - a_{zu,i} \, t_{R}^{2})}{a_{zu,i}^{2}}\right)\\
& \left(\sqrt{\dfrac{(s - a_{zu,i} \, t_{R}^{2})}{a_{zu,i}}}\right)' = - \dfrac{1}{2} \sqrt{\dfrac{a_{zu,i}}{(s - a_{zu,i} \, t_{R}^{2})}} \cdot \left(\dfrac{s}{a_{zu,i}^{2}}\right)
\intertext{ergibt:}
& f'(a_{zu,i}) = \dfrac{3 \, c_{W} \, \rho_{L} \, A_{Proj2} \, l_{LW2}}{2 \, b_{W} \, t_{W}^{2}} \left[2 \, a_{zu,i} \, t_{R}^{2} + 4 \, a_{zu,i} \, t_{R} \, \sqrt{\dfrac{(s - a_{zu,i} \, t_{R}^{2})}{a_{zu,i}}} - \ldots \right.\\
&\left. - 2 \, \dfrac{1}{2} \, a_{zu,i}^{2} \, t_{R} \sqrt{\dfrac{a_{zu,i}}{(s - a_{zu,i} \, t_{R}^{2})}} \, \left(\dfrac{s}{a_{zu,i}^{2}}\right) + s - 2 \, a_{zu,i} \, t_{R}^{2}\right]\\
& f'(a_{zu,i}) = \dfrac{3 \, c_{W} \, \rho_{L} \, A_{Proj2} \, l_{LW2}}{2 \, b_{W} \, t_{W}^{2}} \left[4 \, t_{R} \, \sqrt{a_{zu,i} \, (s-a_{zu,i} \, t_{R}^{2})} - s \, t_{R} \, \sqrt{\dfrac{a_{zu,i}}{(s - a_{zu,i} \, t_{R}^{2})}} + s \right]
\end{align*}
%-----------------------
% Herleitung von t_{B}
%-----------------------
\textbf{\Large{Herleitung der von $t_{B}$}}
\begin{align*}
& t_{B} = \dfrac{- \left(\dfrac{c \, t_{R}^{2}}{2} + a_{1} \, t_{R} \right) \pm \sqrt{\left(- \left(\dfrac{c \, t_{R}^{2}}{2} + a_{1} \, t_{R} \right) \right)^{2} - 4 \, \dfrac{a_{1}}{2} \left( \dfrac{c \, t_{R}^{3}}{2} + a_{1} \dfrac{t_{R}^{2}}{2} - \dfrac{s}{2} \right)}}{2 \, \left( \dfrac{a_{1}}{2} \right)} \hspace{5cm} \phantom{0}\\
\intertext{mit $c = \dfrac{a_{1}}{t_{R}}$:}
& t_{B} = \dfrac{- \left(\dfrac{a_{1} \, t_{R}}{2} + a_{1} \, t_{R} \right) \pm \sqrt{\left(- \left(\dfrac{a_{1} \, t_{R}}{2} + a_{1} \, t_{R} \right) \right)^{2} - 4 \, \dfrac{a_{1}}{2} \left( \dfrac{a_{1} \, t_{R}^{2}}{2} + a_{1} \dfrac{t_{R}^{2}}{2} - \dfrac{s}{2} \right)}}{a_{1}}\\
& t_{B} = \dfrac{- \dfrac{3}{2} \, a_{1} \, t_{R} \pm \sqrt{\left( \dfrac{a_{1} \, t_{R}}{2} \right)^{2} + 2 \, \left( \dfrac{a_{1} \, t_{R}}{2} \right) \, a_{1} \, t_{R} + a_{1}^{2} \, t_{R}^{2} - a_{1}^{2} \, t_{R}^{2} - a_{1}^{2} \, t_{R}^{2} + a_{1} \, s}}{a_{1}}\\
& t_{B} = \dfrac{- \dfrac{3}{2} \, a_{1} \, t_{R} \pm \sqrt{\left( \dfrac{a_{1} \, t_{R}}{2} \right)^{2} + a_{1} \, s}}{a_{1}}\\
& t_{B} = \dfrac{- \dfrac{3}{2} \, a_{1} \, t_{R} \pm \sqrt{\left(\left( \dfrac{t_{R}^{2}}{4} \right) + \dfrac{s}{a_{1}}\right)\, a_{1}^{2}}}{a_{1}}\\
& t_{B} = - \dfrac{3}{2} \, t_{R} + \sqrt{\left( \dfrac{t_{R}^{2}}{4} \right) + \left( \dfrac{s}{a_{1}} \right)}
\end{align*}
\end{document}
schreibe gerade einen Anhang für meine Diplomarbeit. Da leite ich zwei Formeln her. Die Herleitungen stehen in 2 align-Umgebungen. Jede align-Umgebung enthält ca. 6-7 Zeilen. Ich will das die 2 align-Umgebung direkt unter der ersten anfängt und dann umgebrochen wird. Im Moment entsteht aber zwischen beiden Umgebungen ein riesengroßer Abstand und die 2 Umgebung bricht schon nach der ersten um. Habt ihr mich verstanden?
Weiß jemand ne Lösung?
Außerdem würde mich noch interessieren wie ich eine Formel links am Text ausrichte?
Danke im Voraus Gruß der Erbe
Code:
\documentclass[a4paper,11pt,twoside,german]{scrreprt}
\usepackage{amssymb,amsmath}
\usepackage[ngerman]{babel}
\parindent=0cm
\setlength{\voffset}{-10mm}
\setlength{\topmargin}{5mm}
\oddsidemargin=0mm
\evensidemargin=0mm
\setlength{\textwidth}{159.2mm}
\textheight=245mm
\usepackage{setspace}
\onehalfspacing
\begin{document}
\bigskip
\textbf{\Large{Herleitung der Ableitung von $f(a_{zu,i})$}}
\begin{align*}
& f(a_{zu,i}) = \dfrac{3 \, c_{W} \, \rho_{L} \, A_{Proj2} \, l_{LW2}}{2 \, b_{W} \, t_{W}^{2}} \left[a_{zu,i} \, \left(t_{R} + \sqrt{\dfrac{(s - a_{zu,i} \, t_{R}^{2})}{a_{zu,i}}}\right)\right]^{2} - \sigma_{b,zul}\\
& f(a_{zu,i}) = \dfrac{3 \, c_{W} \, \rho_{L} \, A_{Proj2} \, l_{LW2}}{2 \, b_{W} \, t_{W}^{2}} \left[a_{zu,i}^{2} \, t_{R}^{2} + 2 \, a_{zu,i}^{2} \, t_{R} \, \sqrt{\dfrac{(s - a_{zu,i} \, t_{R}^{2})}{a_{zu,i}}} + a_{zu,i}^{2} \, \dfrac{(s - a_{zu,i} \, t_{R}^{2})}{a_{zu,i}}\right] - \sigma_{b,zul}\\
& f(a_{zu,i}) = \dfrac{3 \, c_{W} \, \rho_{L} \, A_{Proj2} \, l_{LW2}}{2 \, b_{W} \, t_{W}^{2}} \left[a_{zu,i}^{2} \, t_{R}^{2} + 2 \, a_{zu,i}^{2} \, t_{R} \, \sqrt{\dfrac{(s - a_{zu,i} \, t_{R}^{2})}{a_{zu,i}}} + a_{zu,i} \, s - a_{zu,i}^{2} \, t_{R}^{2} \right] - \sigma_{b,zul}
\intertext{mit:}
& \left(\sqrt{\dfrac{(s - a_{zu,i} \, t_{R}^{2})}{a_{zu,i}}}\right)' = \dfrac{1}{2} \, \left(\dfrac{(s - a_{zu,i} \, t_{R}^{2})}{a_{zu,i}}\right)^{-\dfrac{1}{2}} \cdot \left(\dfrac{-t_{R}^{2} \, a_{zu,i} - 1 \cdot (s - a_{zu,i} \, t_{R}^{2})}{a_{zu,i}^{2}}\right)\\
& \left(\sqrt{\dfrac{(s - a_{zu,i} \, t_{R}^{2})}{a_{zu,i}}}\right)' = - \dfrac{1}{2} \sqrt{\dfrac{a_{zu,i}}{(s - a_{zu,i} \, t_{R}^{2})}} \cdot \left(\dfrac{s}{a_{zu,i}^{2}}\right)
\intertext{ergibt:}
& f'(a_{zu,i}) = \dfrac{3 \, c_{W} \, \rho_{L} \, A_{Proj2} \, l_{LW2}}{2 \, b_{W} \, t_{W}^{2}} \left[2 \, a_{zu,i} \, t_{R}^{2} + 4 \, a_{zu,i} \, t_{R} \, \sqrt{\dfrac{(s - a_{zu,i} \, t_{R}^{2})}{a_{zu,i}}} - \ldots \right.\\
&\left. - 2 \, \dfrac{1}{2} \, a_{zu,i}^{2} \, t_{R} \sqrt{\dfrac{a_{zu,i}}{(s - a_{zu,i} \, t_{R}^{2})}} \, \left(\dfrac{s}{a_{zu,i}^{2}}\right) + s - 2 \, a_{zu,i} \, t_{R}^{2}\right]\\
& f'(a_{zu,i}) = \dfrac{3 \, c_{W} \, \rho_{L} \, A_{Proj2} \, l_{LW2}}{2 \, b_{W} \, t_{W}^{2}} \left[4 \, t_{R} \, \sqrt{a_{zu,i} \, (s-a_{zu,i} \, t_{R}^{2})} - s \, t_{R} \, \sqrt{\dfrac{a_{zu,i}}{(s - a_{zu,i} \, t_{R}^{2})}} + s \right]
\end{align*}
%-----------------------
% Herleitung von t_{B}
%-----------------------
\textbf{\Large{Herleitung der von $t_{B}$}}
\begin{align*}
& t_{B} = \dfrac{- \left(\dfrac{c \, t_{R}^{2}}{2} + a_{1} \, t_{R} \right) \pm \sqrt{\left(- \left(\dfrac{c \, t_{R}^{2}}{2} + a_{1} \, t_{R} \right) \right)^{2} - 4 \, \dfrac{a_{1}}{2} \left( \dfrac{c \, t_{R}^{3}}{2} + a_{1} \dfrac{t_{R}^{2}}{2} - \dfrac{s}{2} \right)}}{2 \, \left( \dfrac{a_{1}}{2} \right)} \hspace{5cm} \phantom{0}\\
\intertext{mit $c = \dfrac{a_{1}}{t_{R}}$:}
& t_{B} = \dfrac{- \left(\dfrac{a_{1} \, t_{R}}{2} + a_{1} \, t_{R} \right) \pm \sqrt{\left(- \left(\dfrac{a_{1} \, t_{R}}{2} + a_{1} \, t_{R} \right) \right)^{2} - 4 \, \dfrac{a_{1}}{2} \left( \dfrac{a_{1} \, t_{R}^{2}}{2} + a_{1} \dfrac{t_{R}^{2}}{2} - \dfrac{s}{2} \right)}}{a_{1}}\\
& t_{B} = \dfrac{- \dfrac{3}{2} \, a_{1} \, t_{R} \pm \sqrt{\left( \dfrac{a_{1} \, t_{R}}{2} \right)^{2} + 2 \, \left( \dfrac{a_{1} \, t_{R}}{2} \right) \, a_{1} \, t_{R} + a_{1}^{2} \, t_{R}^{2} - a_{1}^{2} \, t_{R}^{2} - a_{1}^{2} \, t_{R}^{2} + a_{1} \, s}}{a_{1}}\\
& t_{B} = \dfrac{- \dfrac{3}{2} \, a_{1} \, t_{R} \pm \sqrt{\left( \dfrac{a_{1} \, t_{R}}{2} \right)^{2} + a_{1} \, s}}{a_{1}}\\
& t_{B} = \dfrac{- \dfrac{3}{2} \, a_{1} \, t_{R} \pm \sqrt{\left(\left( \dfrac{t_{R}^{2}}{4} \right) + \dfrac{s}{a_{1}}\right)\, a_{1}^{2}}}{a_{1}}\\
& t_{B} = - \dfrac{3}{2} \, t_{R} + \sqrt{\left( \dfrac{t_{R}^{2}}{4} \right) + \left( \dfrac{s}{a_{1}} \right)}
\end{align*}
\end{document}